求不定积分∫1 x(4-ln^2x)dx-搜答案-智慧作业帮

∫dx／[x√(4－ln²x)]＝∫dlnx／√(4－ln²x)＝∫dt／√(4－t²)＝∫d(t／2)／√[1－(t／2)²]＝∫dm／√(1－m²

先分布积分,∫ln(x^2+4)dx=xln(x^2+4)-∫xdln(x^2+4)=xln(x^2+4)-∫[2x^2/(x^2+4)]dx=xln(x^2+4)-2∫[x^2/(x^2+4)]dx

原式＝xln(1+x^2)-∫xd[ln(1+x^2)]=xln(1+x^2)-∫2x^2/(1+x^2)dx=xln(1+x^2)-2∫[1-1/(1+x^2)dx=xln(1+x^2)-2x+2a

∫ln(x+√(1+x^2))dxletx=tanadx=(seca)^2da∫ln(x+√(1+x^2))dx=∫(seca)^2ln(tana+seca))da=∫ln(tana+seca))d(

用分步积分∫ln(x^2+1)dx=xln(x^2+1)-∫2x^2/(x^2+1)dx=xln(x^2+1)-∫(2x^2+2-2)/(x^2+1)dx=xln(x^2+1)-∫[2-2/(x^2+

原式=∫ln(x+2)dx²=x²ln(x+2)-∫x²dln(x+2)=x²ln(x+2)-∫(x²-4+4)/(x+2)dx=x²ln(

解∫ln²x/xdx=∫ln²xd(lnx)=∫u²du=1/3u³+C=1/3(lnx)³+C

∫dx/x[根号1-(ln^2)x]=∫d(lnx)/[根号1-(ln^2)x]=∫dt/[根号1-t^2](设t=lnx)=arcsint+C=arcsin(lnx)+C

∫ln(1+x)/(1+x)dx=∫ln(1+x)/(1+x)d(1+x)=∫ln(1+x)dln(1+x)=[ln(1+x)]²/2+C

用分部积分法,(uv)'=u'v+uv',设u=ln(1+x^2),v'=1,u'=2x/(1+x^2),v=x,原式=xln(1+x^2)-2∫x^2dx/(1+x^2)=xln(1+x^2)-2∫

用分部积分法,先把x^2放到dx里面然后分部积分再把dlnx变成1/xdx

∫ln(x+1)dx=∫ln(x+1)d(x+1)=(ln(x+1))(x+1)-∫(x+1)d(ln(x+1))=(x+1)ln(x+1)-∫((x+1)/(x+1))dx=(x+1)ln(x+1)

原式=1/2∫ln(x+1)dx²=1/2*x²ln(x+1)-1/2∫x²dln(x+1)=1/2*x²ln(x+1)-1/2∫x²/(x+1)dx

∫ln2x/x^2dx我可不可以理解为∫(ln2x)/x^2dx不过方法一样∫(ln2x)/x^2dx=-∫(ln2x)d(x^(-1))=-[(ln2x)/x-∫1/xd(ln2x)]=-[(ln2

∫ln(x+√(1+x^2))dx=xln(x+√(1+x^2)-∫xd(ln(x+√(1+x^2))[ln(x+√1+x^2)]'=[1+x/√(1+x^2)]/(x+√(1+x^2))=1/√(1

∫ln(x)/xdx=∫ln(x)/dln(x)=[ln(x)]^2/2+C